Reinstalling Lion (or other) on a 2011 MacBook Air

I have a mid 2011 MacBook Air that I was running High Sierra on (the highest I could update to), I wanted to give it to my sister, as her iMac died, but when I went to reinstall to wipe my data off I found I could not reinstall Lion. I know I did just that about four years ago when I bought an OWC 500 GB SSD for that purpose. Apple has since discontinued Lion. However, you can still download a Lion .dmg from Apple. When I opened it, however, an error read that I could not install without a certificate. Does anyone know how I can get a certificate? Do Third Party vendors sell Lion installers on Flash drives? There is no DVD player so onlne or flash is the only way to go. Also, I have to start with Lion before I can work back up to High Sierra (or maybe El Capitan is fine for her purposes). Could I possibly install Ubuntu or some other Linux?

I have M1 and M3 Macs now, so I don't need the machine. Thanks!